# Profit and Loss Questions

FACTS  AND  FORMULAE  FOR  PROFIT  AND  LOSS  QUESTIONS

Selling Price (SP) : The price at which the shopkeeper sells the goods is called the selling price (SP) of the goods sold by the shopkeeper.

Profit : If the selling price of an article is more than its cost price, then the dealer (or shopkeeper) makes a profit (or gain)

i.e Profit = SP - CP;       SP > CP

Loss : If the selling price of an article is less than its cost price, then the dealer suffers a loss.

i.e loss = CP - SP;        CP > SP

IMPORTANT FORMULAE

1. Profit percentage = $\left(\frac{Profit}{C.P}×100\right)$

2. Loss percentage = $\left(\frac{Loss}{C.P}×100\right)$

3.

4.

5. If an article is sold at a gain of say 35%, then SP = 135% of CP

6. If an article is sold at a loss of say 35%, then SP = 65% of CP

7. When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss given by :

8. If a trader Professes to sell his goods at cost price, but uses false weihts, then

Q:

A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:

 A) No profit, no loss B) 5% C) 8% D) 10%

Explanation:

C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.

S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.

Gain =(80/1600*100) % = 5%

208 35116
Q:

By selling 45 lemons for Rs 40, a man loses 20%. How many should he sell for Rs 24 to gain 20% in the transaction ?

 A) 16 B) 18 C) 20 D) 22

Explanation:

Let S.P. of 45 lemons be Rs. x.

Then, 80 : 40 = 120 : x or   x = $\frac{40×120}{80}$= 60

For Rs.60, lemons sold = 45

For Rs.24, lemons sold  =$\frac{45}{60}×24$= 18.

238 32888
Q:

A shopkeeper cheats to the extent of 10% while buying and selling, by using false weights. His total gain is.

 A) 20% B) 21% C) 22% D) 23%

Explanation:

Gain % = %

=$\left(\frac{{\left(100+10\right)}^{2}}{100}-100\right)$

= 21%

117 27933
Q:

A milkman purchases the milk at Rs. x per litre and sells it at Rs. 2x per litre still he mixes 2 litres water with every 6 litres of pure milk. What is the profit percentage?

 A) 116% B) 166.66% C) 60% D) 100%

Explanation:

Let the cost price of 1-liter pure milk be Re.1, then

8 litre mixture  =>

SP =>  8 x 2 = Rs. 16

Profit % =

164 27255
Q:

The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?

 A) Rs. 2000 B) Rs. 2200 C) Rs. 2400 D) Data inadequate

Explanation:

Let C.P. be Rs. x.

Then,= >$\frac{1920-x}{x}*100=\frac{x-1280}{x}*100$

=>  1920 - x = x - 1280

=>  2x = 3200

=>  x = 1600

Required S.P. = 125% of Rs. 1600 =Rs(125/100*1600) = Rs2000

119 20135
Q:

If the cost price of 12 pens is equal to the selling price of 8 pens, the gain percent is ?

 A) 12% B) 30% C) 50% D) 60%

Explanation:

Friends, we know we will need gain amount to get gain percent, right. So lets get gain first.

Let the cost price of 1 pen is Re 1

Cost of 8 pens = Rs 8

Selling price of 8 pens = 12

Gain = 12 - 8 = 4

Gain% = $\left(\frac{gain}{\mathrm{cos}t}×100\right)$%  = $\left(\frac{4}{8}×100\right)$% = 50%

62 17689
Q:

If books bought at prices ranging from Rs. 200 to Rs. 350 are sold at prices ranging from Rs. 300 to Rs. 425, what is the greatest possible profit that might be made in selling eight books ?

 A) 600 B) 1200 C) 1800 D) none of these

Explanation:

Least Cost Price = Rs. (200 * 8) = Rs. 1600.

Greatest Selling Price = Rs. (425 * 8) = Rs. 3400.

Required profit = Rs. (3400 - 1600) = Rs. 1800.

168 16994
Q:

The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:

 A) 15 B) 16 C) 18 D) 25

Explanation:

Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x

S.P. of x articles = Rs. 20.

Profit = Rs. (20 - x).

$\left(\frac{20-x}{x}*100=25\right)$

=> 2000 - 100x = 25x

=> 125x=2000

=> x=16